Composition operators from the space of Cauchy transforms to Bloch and the little Bloch-type spaces on the unit disk

We completely characterize the boundedness and compactness of composition operators from the space of Cauchy transforms on the unit disk DD, into the Bloch-type space BνBν as well as the little Bloch-type space Bν,0Bν,0, consisting respectively of all holomorphic functions f   on DD such that supz∈Dν(z)|f′(z)|<∞supz∈Dν(z)|f′(z)|<∞, that is, of all holomorphic functions f   on DD such that lim|z|→1ν(z)|f′(z)|=0lim|z|→1ν(z)|f′(z)|=0, for some weight function νν. As a byproduct of our results, norm of the operator is calculated when BνBν is replaced by Bν/CBν/C.